Evidential Domain Adaptation for Remaining Useful Life Prediction with Incomplete Degradation

Data-driven remaining useful life (RUL) prediction requires complete degradation trajectories for training, yet such run-to-failure data are scarce and expensive. Practitioners currently lack principled guidance on how many failure examples suffice for a given model and accuracy target. This paper develops a sample complexity framework for RUL prediction comprising seven main results organised around three themes. First, we establish fundamental learning rates: a distribution-free generalization bound shows that the uniform deviation of the mean squared error decreases as $O(B^{2}\sqrt{p/n})$, where $p$ is the model complexity and $n$ the number of trajectories, and a minimax lower bound proves that the $Θ(p/n)$ rate is unimprovable.} \rev{Second, we quantify how domain knowledge accelerates learning: incorporating degradation physics reduces data requirements by up to two orders of magnitude for deep networks, a Bernstein-type analysis achieves the minimax-optimal $O(p/n)$ rate under high signal-to-noise conditions, and closed-form penalties reveal when an incorrectly assumed physics model hurts rather than helps. Third, we characterise the impact of data quality: fleet variability induces an irreducible bias$-$variance tradeoff, while right-censored observations suffer an efficiency loss that depends critically on the degradation class.} Closed-form expressions are provided for exponential, power-law, and stretched-exponential degradation. \rev{Cross-domain validation against published turbofan, battery, and bearing benchmarks confirms the theoretical predictions within a factor of 2$-$3 on average. The results yield practical guidelines for planning data collection, selecting model complexity, and evaluating physics model assumptions in prognostics applications.

Remaining useful life (RUL) prediction and failure-mode classification are central tasks in predictive maintenance. Many data-driven pipelines use fixed-window supervised learning with complete terminal labels; such routes do not naturally encode the temporal recursion linking successive degradation-state predictions when observations are partial or unit identities are unavailable. We formulate prognostics as vector General Value Function (GVF) prediction on an absorbing degradation process, treating RUL and failure-mode probabilities as temporally consistent targets rather than independent window-level labels, and estimate them with a multi-step temporal-difference estimator, TD($n,λ$). Supporting theory identifies the Bellman fixed point of the vector GVFs, characterizes the linear projected-TD limit and its relation to complete-return Monte Carlo regression under realizability, and explains when bootstrapped TD targets are less variable than Monte Carlo returns. On an event-triggered multimode simulation and NASA C-MAPSS label-scarce stitch data, TD improves RUL and failure-mode prediction relative to a supervised same-backbone Monte Carlo control, especially under scarce complete labels. Practically, fragmented, identity-free degradation records can contribute local Bellman transitions instead of being discarded until complete run-to-failure labels are available.

The construction of high quality health indicators (HIs) is crucial for effective prognostics and health management. Although deep learning has significantly advanced HI modeling, existing approaches often struggle with distribution mismatches resulting from varying operating conditions. Although domain adaptation is typically employed to mitigate these shifts, two critical challenges remain: (1) the misalignment of degradation stages during random mini-batch sampling, resulting in misleading discrepancy losses, and (2) the structural limitations of small-kernel 1D-CNNs in capturing long-range temporal dependencies within complex vibration signals. To address these issues, we propose a domain-adaptive framework comprising degradation stage synchronized batch sampling (DSSBS) and the cross-domain aligned fusion large autoencoder (CAFLAE). DSSBS utilizes kernel change-point detection to segment degradation stages, ensuring that source and target mini-batches are synchronized by their failure phases during alignment. Complementing this, CAFLAE integrates large-kernel temporal feature extraction with cross-attention mechanisms to learn superior domain-invariant representations. The proposed framework was rigorously validated on a Korean defense system dataset and the XJTU-SY bearing dataset, achieving an average performance enhancement of 24.1% over state-of-the-art methods. These results demonstrate that DSSBS improves cross-domain alignment through stage-consistent sampling, whereas CAFLAE offers a high-performance backbone for long-term industrial condition monitoring.